1. Field of the Invention
This disclosure relates to the field of signal processing, and more particularly to improving sub-pixel accuracy and valid signal peak detection for data related to motion between images.
2. Description of the Related Art
Local correlation, covariance, and normalized correlation are among the standard techniques used to recover motion between image frames, such as to derive structure from motion, to track the motion of objects, to resolve stereo vision and in particle image velocimetry, among other applications. Depending on the application, higher accuracy and sensitivity can generally be achieved by interpolating the signal correlation peak with an appropriate function that models the local point spread function (PSF) of the imaging system. For example, in case of diffraction-limited imaging the appropriate interpolating function may be the so-called Airy function, while parabolic or Gaussian functions are also frequently used to simplify interpolation. In most cases the interpolation assumes that the signal is symmetrically distributed around the true correlation peak.
At zero image motion, or when computing the auto-correlation, the signal peak is expected to be symmetric in the small neighborhood of the self-correlation peak. This however is only satisfied if the contributing image features are distributed in the examined local area with sufficient space in between them such that no false correlation takes place between the correlated features; that is, a criterion on the spacing or spatial scale can be formulated that leads to a density requirement on the features under homogeneous distribution. This for example can be used to determine what pattern density is best for actual motion detection. For example, if a 3×3 small neighborhood is used for correlation peak interpolation, no false correlation is allowed to contribute to the values in this small neighborhood of the signal peak. However, this constraint can only be satisfied under artificial or highly controlled circumstances. In images of a real scene, the density of features results in significant false correlation contribution to the small neighborhood of the signal peak. This randomly distorts the signal correlation peak such that it makes the peak asymmetric, resulting in a root mean square (rms) noise in the recovered disparity information even under ideal conditions (e.g. ideal images with integer disparity). The use of a smaller sub-image region for correlation results in a larger rms noise due to lower signal-to-noise ratio in the correlation. This effect can be reduced by low-pass filtering the image with an appropriate filter, but cannot be fully eliminated.
Sub-image cross-correlation (normalized covariance and cross-correlation) inherently gives an asymmetric correlation peak as the true signal representing local image motion between two image frames. This results in the aforementioned rms noise in locating the true correlation signal peak with sub-pixel accuracy, which adversely affects measurement precision. Although an interpolation function might be identified to address bias in estimation of the peak location, one of the underlying problems is stochastic noise in the recovered peak location, which may not exhibit any consistent bias. In addition, enforcing correlation peak symmetry may not itself improve a solution that can only be achieved by additional careful examination and adaptation of the signal peak interpolation procedure.
A need exists for techniques to recover motion between image frames that are less susceptible to rms noise problems.